EduSahara™ Assignment
Name : Distance Formula
Chapter : Distance and Section Formulae
Grade : ICSE Grade X
License : Non Commercial Use
Question
1
1.
Find the distance between the points
(
(
−
1
)
,
4
)
and
(
(
−
8
)
,
(
−
3
)
)
(i)
7
4
√
2
(ii)
7
√
1
2
(iii)
14
(iv)
7
√
4
(v)
7
√
2
Question
2
2.
Find the perimeter of the triangle formed by the points
(
0
,
(
−
1
)
)
,
(
(
−
6
)
,
5
)
and
(
2
,
8
)
(i)
(
6
√
2
+
√
70
+
√
85
)
(ii)
(
6
√
2
+
√
73
+
85
)
(iii)
(
6
√
2
+
√
73
+
4
√
85
)
(iv)
(
6
√
2
+
√
76
+
√
85
)
(v)
(
6
√
2
+
√
73
+
√
85
)
Question
3
3.
Find the lengths of the sides of the triangle formed by the points
(
3
,
(
−
3
)
)
,
(
4
,
(
−
4
)
)
and
(
8
,
(
−
5
)
)
(i)
√
2
,
17
,
√
29
(ii)
√
2
,
√
17
,
√
32
(iii)
4
√
2
,
√
17
,
√
29
(iv)
√
2
,
√
17
,
√
29
Question
4
4.
Distance of the point (1,3) from x-axis is
(i)
3
(ii)
4
(iii)
2
(iv)
1
(v)
(
−
2
)
Question
5
5.
Distance of the given point from x-axis is
(i)
1
(ii)
5
(iii)
-3
(iv)
4
Question
6
6.
Distance of the given point from y-axis is
(i)
5
(ii)
24
(iii)
11
(iv)
3
(v)
8
Question
7
7.
A point lies on positive side of x-axis at a distance of 4 units from y-axis. What are the coordinates of the point?
(i)
(
0
,
4
)
(ii)
(
0
,
(
−
4
)
)
(iii)
(
4
,
0
)
(iv)
(
(
−
4
)
,
0
)
Question
8
8.
A point lies on negative side of x-axis at a distance of 1 units from y-axis. What are the coordinates of the point?
(i)
(
(
−
1
)
,
0
)
(ii)
(
0
,
(
−
1
)
)
(iii)
(
0
,
1
)
(iv)
(
1
,
0
)
Question
9
9.
A point lies on positive side of y-axis at a distance of 8 units from x-axis. What are the coordinates of the point?
(i)
(
0
,
(
−
8
)
)
(ii)
(
(
−
8
)
,
0
)
(iii)
(
0
,
8
)
(iv)
(
8
,
0
)
Question
10
10.
A point lies on negative side of y-axis at a distance of 6 units from x-axis. What are the coordinates of the point?
(i)
(
0
,
6
)
(ii)
(
0
,
(
−
6
)
)
(iii)
(
(
−
6
)
,
0
)
(iv)
(
6
,
0
)
Question
11
11.
Find the distance of the point
(
(
−
1
)
,
(
−
3
)
)
from origin
(i)
10
(ii)
√
7
(iii)
√
10
(iv)
4
√
10
(v)
√
12
Question
12
12.
A is a point on x-axis with abscissa
(-6)
and B is a point on y-axis
with ordinate
(-7)
.
Find the distance between A and B
(i)
√
85
(ii)
√
83
(iii)
4
√
85
(iv)
√
88
(v)
85
Question
13
13.
KM is the straight line of length
√
13
units.
If K has the coordinates
(
2
,
4
)
and M has coordinates
(k,2)
,
find the possible values of k
(i)
(
7
,
1
)
(ii)
(
5
,
(
−
1
)
)
(iii)
(
3
,
(
−
3
)
)
(iv)
(
4
,
0
)
(v)
(
6
,
(
−
2
)
)
Question
14
14.
Find the point on x-axis which is equidistant
from the points
(
1
,
(
−
1
)
)
and
(
4
,
4
)
(i)
(
6
,
(
−
1
)
)
(ii)
(
7
,
2
)
(iii)
(
4
,
1
)
(iv)
(
3
,
(
−
2
)
)
(v)
(
5
,
0
)
Question
15
15.
Find the point on y-axis which is equidistant
from the points
(
(
−
8
)
,
(
−
6
)
)
and
(
(
−
3
)
,
(
−
5
)
)
(i)
(
1
,
(
−
34
)
)
(ii)
(
(
−
1
)
,
(
−
32
)
)
(iii)
(
(
−
2
)
,
(
−
35
)
)
(iv)
(
0
,
(
−
33
)
)
(v)
(
2
,
(
−
31
)
)
Question
16
16.
Find the points on x-axis,
which are at a distance of
14
units
from the point
(
(
−
7
)
,
(
−
6
)
)
(i)
(
(
−
9
+
4
√
10
)
,
(
−
2
)
)
,
(
(
−
7
−
4
√
10
)
,
0
)
(ii)
(
(
−
6
+
4
√
10
)
,
(
−
1
)
)
,
(
(
−
7
−
4
√
10
)
,
0
)
(iii)
(
(
−
5
+
4
√
10
)
,
2
)
,
(
(
−
7
−
4
√
10
)
,
0
)
(iv)
(
(
−
7
+
4
√
10
)
,
0
)
,
(
(
−
8
−
4
√
10
)
,
1
)
(v)
(
(
−
7
+
4
√
10
)
,
0
)
,
(
(
−
7
−
4
√
10
)
,
0
)
Question
17
17.
Find the points on y-axis,
which are at a distance of
10
units
from the point
(
(
−
7
)
,
(
−
1
)
)
(i)
(
2
,
(
1
+
√
51
)
)
,
(
0
,
(
−
1
−
√
51
)
)
(ii)
(
(
−
2
)
,
(
−
3
+
√
51
)
)
,
(
0
,
(
−
1
−
√
51
)
)
(iii)
(
1
,
(
−
2
+
√
51
)
)
,
(
0
,
(
−
1
−
√
51
)
)
(iv)
(
0
,
(
−
1
+
√
51
)
)
,
(
0
,
(
−
1
−
√
51
)
)
(v)
(
0
,
(
−
1
+
√
51
)
)
,
(
(
−
1
)
,
(
−
√
51
)
)
Question
18
18.
Find the lengths of the medians of a triangle whose vertices are
(
(
−
7
)
,
5
)
,
(
(
−
7
)
,
7
)
and
(
(
−
2
)
,
(
−
6
)
)
(i)
1
2
√
194
,
1
2
√
146
,
1
(ii)
1
2
√
106
,
5
2
√
10
,
13
(iii)
1
,
1
2
√
194
,
1
2
√
194
Question
19
19.
If point P
(
(
−
6
7
)
,
6
)
is equidistant from the points
(a,-8)
and
(
8
,
(
−
6
)
)
, find a
(i)
-7
(ii)
-4
(iii)
-6
(iv)
-5
(v)
-8
Question
20
20.
If point P
(x,3)
is equidistant from the points
(
(
−
8
)
,
8
)
and
(
(
−
4
)
,
5
)
, find x
(i)
(
-71
8
)
(ii)
(
-67
8
)
(iii)
(
-53
6
)
(iv)
(
-69
8
)
(v)
(
-17
2
)
Question
21
21.
Find the relation between x and y such that the point P
(
x
,
y
)
is equidistant from points
(
(
−
5
)
,
0
)
and
(
8
,
(
−
6
)
)
(i)
(
−
27
x
+
12
y
+
75
)
=
0
(ii)
(
−
26
x
+
15
y
+
75
)
=
0
(iii)
(
−
26
x
+
12
y
+
75
)
=
0
(iv)
(
−
7
x
−
14
y
−
35
)
=
0
(v)
(
−
7
x
−
12
y
−
35
)
=
0
Assignment Key
1) (v)
2) (v)
3) (iv)
4) (i)
5) (i)
6) (v)
7) (iii)
8) (i)
9) (iii)
10) (ii)
11) (iii)
12) (i)
13) (ii)
14) (v)
15) (iv)
16) (v)
17) (iv)
18) (ii)
19) (iii)
20) (iv)
21) (iii)
